Dr Sam Jelbart
Lecturer
School of Mathematical Sciences
College of Sciences
Eligible to supervise Masters and PhD (as Co-Supervisor) - email supervisor to discuss availability.
I am an applied mathematician with a background in the analysis of dynamical systems characterised by multiple time-scales and abrupt transitions. The use of geometric methods is a common theme in my research.I have expertise in the analysis of ordinary differential equations and non-smooth systems, but a broader interest in the dynamics of maps, partial differential equations and non-autonomous systems. More recently I have been working on rigorous geometric approaches to model reduction in complex dynamical systems with applications in systems biology.
My research is aimed at understanding the behaviour of applied dynamical systems, with a particular emphasis on identifying and utilising structure associated with multiple scales and/or the loss of smoothness. A lot of my research is driven by a long term goal to develop and apply rigorous geometric methods to the study of complex systems, with an eye towards understanding the dynamics of problems of high social and scientific significance in, e.g., climate, biological and biophysical systems.
My PhD focused on planar but highly 'singular' dynamical systems, where I developed expertise in Geometric Singular Perturbation Theory and a method of desingularisation known as geometric blow-up. During my time as a postdoc in Munich and Vienna, I applied this knowledge to dynamical systems with more than two time-scales (both generally and in the context of models for intracellular calcium oscillations), discrete dynamical systems, partial differential equations and non-autonomous systems.
More recently, I have been interested in the development and application of novel geometric methods to the study of complex dynamical processes arising in the study of gene regulatory networks and other models in systems biology.
| Date | Position | Institution name |
|---|---|---|
| 2024 - 2024 | Postdoctoral Fellow | Vienna university of technology |
| 2021 - 2024 | Postdoctoral Researcher | Technical University of Munich |
| 2017 - 2020 | PhD Student (applied mathematics) | University of Sydney |
| Language | Competency |
|---|---|
| English | Can read, write, speak, understand spoken and peer review |
| German | Can read, speak and understand spoken |
| Date | Institution name | Country | Title |
|---|---|---|---|
| University of Sydney | Australia | PhD (Applied Mathematics) | |
| University of Sydney | Australia | Honours (Applied Mathematics) | |
| University of Sydney | Australia | BA Arts & Science (Majors: Mathematics, Physics, Philosophy) |
| Year | Citation |
|---|---|
| 2025 | Hummel, F., Jelbart, S., & Kuehn, C. (2025). Geometric blow-up of a dynamic Turing instability in the Swift-Hohenberg equation. Journal of Differential Equations, 427, 219-309. Scopus2 WoS4 |
| 2025 | Rahmani, B., Jelbart, S., Kirk, V., & Sneyd, J. (2025). Understanding Broad-Spike Oscillations in a Model of Intracellular Calcium Dynamics. SIAM Journal on Applied Dynamical Systems, 24(1), 131-164. Scopus2 |
| 2025 | Jelbart, S., Kristiansen, K. U., & Szmolyan, P. (2025). Traveling Waves and Exponential Nonlinearities in the Zeldovich–Frank-Kamenetskii Equation. SIAM Journal on Applied Dynamical Systems, 24(1), 530-556. |
| 2025 | Rahmani, B., Jelbart, S., Kirk, V., & Sneyd, J. (2025). Understanding Broad-Spike Oscillations in a Model of Intracellular Calcium Dynamics. SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, 24(1), 131-164. WoS2 |
| 2025 | Jelbart, S., Kristiansen, K. U., & Szmolyan, P. (2025). Switching, multiple time-scales and geometric blow-up in a low-dimensional gene regulatory network.. Journal of mathematical biology, 92(1), 23. |
| 2024 | Jelbart, S., & Kuehn, C. (2024). Extending discrete geometric singular perturbation theory to non-hyperbolic points. Nonlinearity, 37(10), 49 pages. Scopus1 WoS1 |
| 2024 | Jelbart, S. (2024). Rate and Bifurcation Induced Transitions in Asymptotically Slow-Fast Systems. SIAM Journal on Applied Dynamical Systems, 23(3), 1836-1869. Scopus1 WoS1 |
| 2024 | Jelbart, S., Kuehn, C., & Kuntz, S. V. (2024). Geometric Blow-Up for Folded Limit Cycle Manifolds in Three Time-Scale Systems. Journal of Nonlinear Science, 34(1), 68 pages. Scopus2 WoS1 |
| 2023 | Jelbart, S., & Kuehn, C. (2023). DISCRETE GEOMETRIC SINGULAR PERTURBATION THEORY. Discrete and Continuous Dynamical Systems- Series A, 43(1), 57-120. Scopus9 WoS7 |
| 2022 | Jelbart, S., Pages, N., Kirk, V., Sneyd, J., & Wechselberger, M. (2022). Process-Oriented Geometric Singular Perturbation Theory and Calcium Dynamics. SIAM Journal on Applied Dynamical Systems, 21(2), 982-1029. Scopus8 WoS8 |
| 2022 | Jelbart, S., Kristiansen, K. U., Szmolyan, P., & Wechselberger, M. (2022). Singularly Perturbed Oscillators with Exponential Nonlinearities. Journal of Dynamics and Differential Equations, 34(3), 1823-1875. Scopus7 WoS9 |
| 2021 | Jelbart, S., Kristiansen, K. U., & Wechselberger, M. (2021). Singularly perturbed boundary-focus bifurcations. Journal of Differential Equations, 296, 412-492. Scopus14 WoS15 |
| 2021 | Jelbart, S. (2021). BEYOND SLOW-FAST: RELAXATION OSCILLATIONS in SINGULARLY PERTURBED NONSMOOTH SYSTEMS. Bulletin of the Australian Mathematical Society, 104(2), 342-343. WoS1 |
| 2021 | Jelbart, S., Kristiansen, K. U., & Wechselberger, M. (2021). Singularly perturbed boundary-equilibrium bifurcations. Nonlinearity, 34(11), 7371-7414. Scopus15 WoS16 |
| 2020 | Jelbart, S., & Wechselberger, M. (2020). Two-stroke relaxation oscillators. Nonlinearity, 33(5), 2364-2408. Scopus21 WoS22 |
| Year | Citation |
|---|---|
| 2024 | Jelbart, S., & Kuehn, C. (2024). A formal geometric blow-up method for pattern forming systems. In Contemporary Mathematics Vol. 806 (pp. 49-86). Banff: American Mathematical Society. DOI Scopus2 |
| Year | Citation |
|---|---|
| 2025 | Jelbart, S., Kristiansen, K. U., & Szmolyan, P. (2025). Switching, Multiple Time-Scales and Geometric Blow-Up in a Low-Dimensional Gene Regulatory Network. |
| 2024 | Jelbart, S. (2024). Rate and Bifurcation Induced Transitions in Asymptotically Slow-Fast Systems. |
| 2024 | Jelbart, S., Kuehn, C., & Sánchez, A. M. (2024). Characterising exchange of stability in scalar reaction-diffusion equations via geometric blow-up. |
| 2024 | Jelbart, S., Kristiansen, K. U., & Szmolyan, P. (2024). Travelling Waves and Exponential Nonlinearities in the Zeldovich-Frank-Kamenetskii Equation. |
| 2024 | Rahmani, B., Jelbart, S., Kirk, V., & Sneyd, J. (2024). Understanding broad-spike oscillations in a model of intracellular calcium dynamics. |
| 2023 | Jelbart, S., & Kuehn, C. (2023). A Formal Geometric Blow-up Method for Pattern Forming Systems. |
| 2023 | Jelbart, S., & Kuehn, C. (2023). Extending Discrete Geometric Singular Perturbation Theory to Non-Hyperbolic Points. |
| 2022 | Hummel, F., Jelbart, S., & Kuehn, C. (2022). Geometric blow-up of a dynamic Turing instability in the Swift-Hohenberg equation. |
| 2022 | Kuntz, S. -V., Jelbart, S., & Kuehn, C. (2022). Geometric Blow-up for Folded Limit Cycle Manifolds in Three Time-Scale Systems. DOI |
| 2022 | Jelbart, S., & Kuehn, C. (2022). Discrete Geometric Singular Perturbation Theory. |
| 2021 | Jelbart, S., Pages, N., Kirk, V., Sneyd, J., & Wechselberger, M. (2021). Process-Oriented Geometric Singular Perturbation Theory and Calcium Dynamics. |
| 2021 | Jelbart, S., Kristiansen, K. U., & Wechselberger, M. (2021). Singularly Perturbed Boundary-Equilibrium Bifurcations. |
| 2020 | Jelbart, S., Kristiansen, K. U., & Wechselberger, M. (2020). Singularly Perturbed Boundary-Focus Bifurcations. |
| 2019 | Jelbart, S., Kristiansen, K. U., Szmolyan, P., & Wechselberger, M. (2019). Singularly Perturbed Oscillators with Exponential Nonlinearities. |
| 2019 | Jelbart, S., & Wechselberger, M. (2019). Two-Stroke Relaxation Oscillators. |
I was awarded a prestigious Marie Curie Fellowship to work on the project Model Reduction for Complex Systems with Exponential Nonlinearity via Geometric Singular Perturbation Theory https://cordis.europa.eu/project/id/101103827. The fellowship is valued at just under 200,000 Euro over two years.
| Date | Role | Research Topic | Program | Degree Type | Student Load | Student Name |
|---|---|---|---|---|---|---|
| 2025 | Co-Supervisor | Geometric Blow-up Techniques for the Study of Switching in Multi-Scale Systems | Doctor of Philosophy | Doctorate | Full Time | Mr Tyson Jack Rowe |
| 2025 | Co-Supervisor | Geometric Blow-up Techniques for the Study of Switching in Multi-Scale Systems | Doctor of Philosophy | Doctorate | Full Time | Mr Tyson Jack Rowe |
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